Real Lagrangians in toric degenerations

One of the main tools of the Gross-Siebert program in mirror symmetry is toric degenerations constructed from integral affine manifolds with singularities. The real loci of such degenerations provide interesting examples of Lagrangians which conjecturally are amenable to algebraic-geometric versions of Floer theory. In this talk I will discuss how the topology of the real locus can be understood by means of affine geometry and by Kato-Nakayama spaces associated to log spaces. This talk reports on joint work with Bernd Siebert.